Math Is Fun Forum

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

circle lengths

In the adjoining figure,  AB is tangent at  A to the circle with center O , point D is interior to the circle, and DB intersects the circle at C. If BC = DC = 3,OD = 2 , and AB = 6, then find the radius of the circle.

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I see you have graph paper.
You must be plotting something

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: circle lengths

Hi cooljackiec;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: circle lengths

thanks. can you help me on this?

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I see you have graph paper.
You must be plotting something

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: circle lengths

hi

There's a theorem that is true for all circles.  For any four points on the circumference, see diagram

AE x EC = DE x EB

That should be enough for you to do this one.

Bob

ps.  to prove it look for equal angles using the circle theorems and then similar triangles.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: circle lengths

hmm.. that is the power of a point theorem right?? i think it works for secants/tagents too

---

I see you have graph paper.
You must be plotting something

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: circle lengths

I've not met it called that, but Wiki agrees with you:

http://en.wikipedia.org/wiki/Power_of_a_point

And yes it does apply to tangents.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: circle lengths

still stuck

---

I see you have graph paper.
You must be plotting something

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: circle lengths

Hi;

I got an answer of 31 by another method. Can you check it?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: circle lengths

seems correct. how did you do that?

---

I see you have graph paper.
You must be plotting something

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: circle lengths

I have been experimenting with the team of bobbym and geogebra, trying to be more than an amazed bystander. The great gAr would describe it as a "mathod!"

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: circle lengths

hi cooljackiec

still stuck

I'm assuming you mean with the question in post 3.

I put x = XP and y = QY.

Then applied the theorem twice:

5 x 6 = x(27+y)
7 x 12 = (x+27)y

I subtracted to eliminate xy.

Then made y the subject of that and substituted back into one equation to make a quadratic.

It factorised easily with one positive and one negative root.  Rejected the negative and then substituted back to find y.

Got the same answer as bobbym. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

grace_rong

Member

Registered: 2016-08-12

Posts: 2

Re: circle lengths

Hi bobbym,

Do you mind telling me how you solved the first problem? 

Thanks,

Grace

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: circle lengths

Hi grace_rong;

Welcome to the forum. That was done more than 3 years ago. See post #10.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: circle lengths

Last edited by thickhead (2016-08-12 19:04:27)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

grace_rong

Member

Registered: 2016-08-12

Posts: 2

Re: circle lengths

Thanks thickhead and bobbym!